Respuesta :
To find the surface area of the cube that will be blue and yellow, we need to consider the area covered by the blue circles and the area not covered by them.
a) **Blue Area:**
Each face of the cube has an area of \(2 \times 2 = 4 \text{ ft}^2\). Since there are 6 faces, the total surface area of the cube is \(6 \times 4 = 24 \text{ ft}^2\). The area covered by the blue circles on each face is the area of a circle with a radius of 1 ft, which is \(\pi r^2 = \pi \times (1)^2 = \pi \text{ ft}^2\). Since there are 6 faces and each face is covered with a blue circle, the total blue area is \(6 \times \pi \text{ ft}^2\).
b) **Yellow Area:**
The area of the cube not covered by the blue circles is the total surface area of the cube minus the total area covered by the blue circles. So, the yellow area is \(24 \text{ ft}^2 - 6 \times \pi \text{ ft}^2\).
Now, we can calculate the numerical values:
a) Blue area: \(6 \times \pi \approx 18.85 \text{ ft}^2\)
b) Yellow area: \(24 \text{ ft}^2 - 6 \times \pi \approx 5.15 \text{ ft}^2\).
a) **Blue Area:**
Each face of the cube has an area of \(2 \times 2 = 4 \text{ ft}^2\). Since there are 6 faces, the total surface area of the cube is \(6 \times 4 = 24 \text{ ft}^2\). The area covered by the blue circles on each face is the area of a circle with a radius of 1 ft, which is \(\pi r^2 = \pi \times (1)^2 = \pi \text{ ft}^2\). Since there are 6 faces and each face is covered with a blue circle, the total blue area is \(6 \times \pi \text{ ft}^2\).
b) **Yellow Area:**
The area of the cube not covered by the blue circles is the total surface area of the cube minus the total area covered by the blue circles. So, the yellow area is \(24 \text{ ft}^2 - 6 \times \pi \text{ ft}^2\).
Now, we can calculate the numerical values:
a) Blue area: \(6 \times \pi \approx 18.85 \text{ ft}^2\)
b) Yellow area: \(24 \text{ ft}^2 - 6 \times \pi \approx 5.15 \text{ ft}^2\).
